guns fired up only half deadly.

Some may say this is bad evidence however the mythbusters did show that a 7.62mm bullet fired directly upwards would reach the pinical of its tragectory and then tumble back to earth taking more then twice the time and at less then half the speed (40 instead of 17 seconds). as a bullet has a very small mass it requires a huge amount of speed to make up the momentum it needs to cause the massive internal damage they do when fired.

the tumbling causes the bullet to reach a much slower terminal velocity then the initial fireing and therefore would not be at a deadly speed on impact with the ground or a person. much in the same way that a naturally falling 1p coin would be completely harmless no matter how high you dropped it from. sure it would sting like buggery and probably even pierce the skin however it would not pierce your skull so you would survive.

this is distinct from bullets fired at an angle close but not quite vertically which can hold their parabolic path and therefore their stabilizing rotation allowing them to return to earth at the same speed that they left the gun therefor being deadlly.

as evidence i will mention that fry says it takes 17 seconds for a 7.62mm to go up and 40 to come back down. if the bullet was coming down in a deadly point first manner physics (specifically the laws of concervation of energy) states it would take about the same amount of time to come back down (well a little bit slower due to the small amount of drag lets say 20 seconds) which is what happens when the bullet is fired at an angle. its these bullets that cause deaths because very few people actualy manage to shoot perfectly verticaly.

so to summerise bullets fired perfectly vertically not deadly
bullets fired at a alight angle keep their speed and stability and are deadly but for someone a long way from the shooter.

Thanks for that, Milamber. Here's what we had in mind on the show: by the time the bullet gets back to ground level it's doing about 70 metres per second (falling base first, because itís more stable that way round). The bullet velocity required for skin penetration is between 45 and 60 metres per second, but a blow to the head doesnít need to penetrate the skin in order to be fatal, and this is the key: the reason fatalities are disproportionate is that any injuries which do occur are likely to be cranial (so you may be less likely to be hit than if somebody is aiming at you, but if you are hit itís more likely to be fatal Ė about five times as likely as in normal firing).

ahh but the center of gravity of a 7.62 (and of a handgun bullet) is NOT at the base of the bullet as u described its about 2/3 the way from the tip making its most stable way of falling is on its side making its terminal velcity only about 44 m/s. given that its liable to tumble that brings it up to a max of about 50m/s thats still a sizable gap from your predicted 70m/s and making it much less likly to cause a fatal injury.

what you also forgot to take into account is the aerodynamic center of the bullet. when facing tail down the flat surface the bullet presents is a easy target for a moment to be created rotating the bullet quite easily at those speeds about its center of mass causeing it to tumble end on end. where as on its side the bullet can be easily rotated about its long axis however it makes no aerodynamic difference because its cylindrical and its still presenting a large area to the air.

Boy killed by bullet 'fired three miles away'Telegraph 3rd Jan 2010
Marquel Peters was seated with his parents inside a church in Decatur, Georgia, when a bullet came through the roof and struck his head.
The toddler collapsed at the feet of his parents, who had no idea what caused a gaping wound in his head.
It was only after doctors removed the bullet as they tried in vain to save his life that they realised he had been shot.

Italian boy shot by falling bullet in Miami New Year celebrationsTelegraph 4th Jan 2010
Andrea Fregonese was released from the intensive care unit of Jackson Memorial Hospital on Sunday, but remains in hospital for treatment of his chest wound.
Andrea and his parents, from Treviso, Italy, were sitting at an outside restaurant when the 6-year-old complained of chest pains shortly after midnight. When his parents inspected his body, they discovered a bullet entry wound.

My quibble is about the horizontal firing and dropping of a bullet from the same height.

It is true that the horizontally fired bullet and the dropped bullet would hit the surface at the same moment, if the experiment happens in vacuum. In a vacuum gravity is the only affecting force and it affects both objects in the same way.

However if the shooting occurs in a normal atmosphere then there is the additional force of drag.

Both bullets will experience drag. The difference however is, that the horizontally fired bullet has a much higher velocity. Only the "downward" velocity components vy at t=0 are the same (vy=0) for both bullets.

The force of drag is (roughly) proportional to the square of the velocity v (v = sqrt(vx2 + vy2)) and not only to the vy component. Thus, the drag experienced by the fired bullet is much higher than the drag experienced by the dropped bullet. As a consequence the fired bullet will reach the surface fractionally later.

If we use a hypothetical "ball"/"shot".

a ball of 10mm diameter, 10g mass, fired at 500m/s from a height of 10m

those of these reports are of situations where the bullet DID NOT go perfectly vertical and in fact was fired off vertical and thus traveled a parabolic path for some distance.

in these cases being fired at an angle as little as 2 degrees from vertical is enough for the bullet to return to earth while retaining its stabilising spin from the rifleing however that would mean it arrives at the earth point first and moving at an only slightly reduced speed as when it left the gun

i said that in my original post.

you will notice also that its actually quite unnatural for someone to fire perfectly vertically and given that fact you can assume that most bullets are fired at an angle greater then 2 degrees and therefore return to earth in a deadly fasion miles from its point of origin. this does not mean a FALLING bullet is deadly however its that a FIRED bullet is deadly. the fact that the bullet is coming down point first in such cases means that its terminal velocity is much faster then a normal falling bullet and thus frys figures for a deadly falling bullet of 17 up and 40 down are wrong it should be either 17 up and 20 down for deadly or something more like 60 seconds (i didnt do the maths) for a free falling.

And once again id hate to use the mythbusters as evidence (as sometimes their methods are a little wonky) however if u watch season 4 ep 7 they go through it quite thoughly and i would say quite a scientifically sound manner they even speak to an expert doctor who explains how people get hit.

and also simple observation shows the center of mass on a bullet is about 2/3 the way along as a bullet is of uniform mass. i cant be bothered doing the math to prove it as its bleeding obvious anyway.

My quibble is about the horizontal firing and dropping of a bullet from the same height.

An idealized bullet that doesn't spin and follows a perfect ballistic trajectory will hit the ground at the same time as one that's dropped.

A real bullet fired from a smoothbore with no additional stablization may hit faster or slower depending on how it decides to come out of the barrel. You can't really predict how it flies.

A bullet that is made to spin, either from rifling in the barrel or fins like a sabot round from the gun on an American Abrams tank will hit after the bullet you drop because spinning bullets rise before falling. 200 yards from the gun it's fired from a .30-06 bullet will still generally be two inches above the barrel. In the same period of time a typical .22 long rifle bullet will have travelled less than half as far horizontally and will be at a point 5 or so inches closer to the ground, but both will still be at least a little above the dropped bullet.

The answer that was given on the show was both true and false depending on how you frame the question. You need a bullet that doesn't have any upward forces on it.

i dont actually have a problem with the whole bullets both hitting ground at the same time because it is a physics theorem designed to teach people the very basics of vector physics and not to be taken literaly.

you can quibble about hundreths off a second but the idea in this case is to give an idea to the general public about how gravity works and that horesontal speed and gravitational acceleration are seperate things which is why they hit at the same time. the fact that the real world is involved tends to screw up 99.99% of all physics theorys which only work exactly spot on perfect in a vacuum, in a fariday cage and devoid of outside influence.

As it was explained to me - bullets like any other object are affected by gravity, and, when they leave the barrel, they no longer have any physical support, i.e the barrel, so they begin to fall. In addition, they are travelling through air, so air resistance progressively slows their flight. On most occasions the barrel is slanted upward slightly to compensate for this immediate drop; thus since the barrel is aimed slightly upward, the bullet does, indeed, rise slightly after it leaves the barrel, but the bullet never rises above the axis of the barrel.
Rifling / spin may slow the rate of fall, but they do not cause the bullet to "rise".

Milamber wrote:

i dont actually have a problem with the whole bullets both hitting ground at the same time because it is a physics theorem designed to teach people the very basics of vector physics and not to be taken literaly.

We'll have to disagree about that when you are talking of an event that lasts not much more than a second, tenths of a second constitute a sizeable difference to my mind.

We'll have to disagree about that when you are talking of an event that lasts not much more than a second, tenths of a second constitute a sizeable difference to my mind.

but the idea behind it isnt to describe the specific situation the same thing is true of a ships cannon shells in the same situation from 1000 meters in the air. the explanation is purly a conceptual proof to explain the IDEA of a universal gravitational acceleration to someone who doesnt already have any idea about vector physics. and for us to be trying to pull apart the specific situation is pointless because its not designed for us its designed for someone who doesnt or has not study physics.

its the same as an engeneer useing special relitivity to design a toy. its just not nesissary.

so to summerise bullets fired perfectly vertically not deadly
bullets fired at a alight angle keep their speed and stability and are deadly but for someone a long way from the shooter.

To be fair to the show, the question asked was whether it was a good idea to fire guns into the air in celebration. It didn't address the specific case of a bullet fired perfectly vertically into the air.

Also, I would refer you to the publication "Spent bullets and their injuries: the result of firing weapons into the sky" by Ordog et al published in the December 1994 edition of the Journal of Trauma which states:

"When the bullet reaches the top of its flight, it is still spinning, and if it is stable it falls back base first. Occasionally, it falls back either point first or tumbles, thus either decreasing or increasing its flight time. With a very sharply pointed bullet, the resistance on the bullet is less, and on the square base much greater, so that bullets coming down nose first fall faster than those that fall base first, but even so, a 150-grain, .30-caliber bullet tends to balance its weight against the air resistance at a velocity of about 300 fps."

300 feet per second is otherwise known to us metric types as 90 metres per second.

The article concludes with the sentence:

"Although the terminal velocity is low (between 300 and 600 fps) and the terminal kinetic energy low (30 to 60 foot-pounds), they are enough to cause significant intracranial, and occasionally, chest injuries."

Of the 118 patients at the King/Drew Medical Center in LA studied in the article, 40% of those with head wounds and 50% of those with posterior chest wounds died as a result of their injuries.

the problem is that a bullet NEVER falls base first. no bullet ever falls stabally in that way thus the figures they gave were incorrect.

a bullet either falls point first at the same rate it went up on a balistic trajectory OR it falls on its side at about 44m/s (this is the terminal velocity of both 30.06 and 9mm.

the reason for this is that a bullet gets its stability according to aerodynamicaly forces about its moment of inertia (very close to its center of mass) which is near the center of the bullet. when the bullet is falling flat end down it comes under a force about its edges causeing a moment about its COM. if the COM is near the bass of the bullet this is easily counteracted by a small force at the tip of the bullet pushing it back vertically.

if the COM is near the center of the bullet the correcting force isnt big enough to counteract the rotation force untill the bullet is mostly horezontal therefor the bullet falls most stabilly horezontally giving a maximum drag coefficient possible and slowing the bullet down BELOW the quoted 70m/s that the elves described.

this makes all their calculations wrong and the reasons people die an incorrect way and thats what i have an issue with.